Merge pull request #9 from volf52/master

Combinations without using factorials-Python

Author: rawktron

recipes/Python/Combination without using factorials/LICENSE

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+MIT License
+
+Copyright (c) 2017 Muhammad Arslan <rslnkrmt2552@gmail.com>
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

recipes/Python/Combination without using factorials/README.md

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+Created on 2017-09-02
+
+Author : Muhammad Arslan <rslnkrmt@gmail.com>
+
+Licence : MIT
+
+Finding the number of combinations (nCr) without use of factorials
+------------------------------------------------------------------
+
+Using factorials recursively can greatly reduce performance and use a lot of memory especially when finding nCr of large sets. This aims to correct that to some extent.
+Enjoy and provide me with suggestions if any.

recipes/Python/Combination without using factorials/combo.py

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+import operator as op
+
+
+def ncr(n, r):
+    r       = min(r, n-r)
+    if x == 0: return 1
+    num     = reduce(op.mul, xrange(n, n-1, -1))
+    denom   = reduce(op.mul, xrange(1, r+1))
+    return num // denom